There was an ABC News interview (transcript) with George Stephanopoulos that aired on This Week 7/31/2016, the day before his Ohio speech. It aired around 10:30am ET so I am assuming that it was recorded the day before. I say this as a qualification for being as close to his 'initial' public reaction as we can get.
Around the 14:30 mark of that interview came this exchange:
[clips of Khan's speech at DNC]
GS: He said you wouldn't have even let his son in America. He...
DT: He doesn't know that. I saw him, he was, you know, very emotional and probably looked like a nice guy to me. His wife, if you look at his wife, she was standing there, she had nothing to say, she probably maybe she wasn't allowed to have anything to say you tell me, but plenty of people have written that. She was extremely quiet and it looked like she had nothing to say, a lot of people have said that, and, personally, I watched him, I wish him the best of luck George.
GS: What would you say to that father?
DT: Well I'd say we've had a lot of problems with radical Islamic terrorism, that's what I'd say. We have a lot of problems where you look at San Bernardino, you look at Orlando, you look at the World Trade Center, you look at so many different things, you look at what happened to the priest over the weekend in Paris where his throat was cut, 85 year old beloved Catholic priest, you look at what happened in Nice, France a couple of weeks ago, I'd say you got to take a look at that because somethings going on and it's not good.
GS: He said you have sacrificed nothing and no one.
DT: Well that sounds, who wrote that, did Hillary's script writers write it? Because everybody that went out there, we also had John Allen who failed with ISIS. I mean he was a General, Allen, General Allen, he went out, and he was ranting and raving and then I read a report. He was in there for a number of months and he failed with ISIS and he's telling me...
There is a bit more context about his reaction to Khan in the interview after talking about John Allen, but I wanted to include at least the start of the exchange as text in this answer.